Category:Definitions/Complex Powers

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This category contains definitions related to Complex Powers.
Related results can be found in Category:Complex Powers.


Let $z, k \in \C$ be any complex numbers.


$z$ to the power of $k$ is defined as the multifunction:

$z^k := e^{k \ln \paren z}$

where $e^z$ is the exponential function and $\ln$ is the natural logarithm multifunction.